# Matrix fundamentals under time pressure

> ML preparation item.

- Stable ID: `original-la-foundations`
- Area: Mathematics
- Topic: Linear Algebra
- Origin: original
- Expected time: 8 minutes
- Skills: matrix-operations, inverse, determinant-trace, matrix-norms
- Item JSON: https://mlprep.iwase.dev/data/items/original-la-foundations.json

## Problem

Let
$$
A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}.
$$
Compute $\det(A)$, $\operatorname{tr}(A)$, $A^{-1}$, and the Frobenius norm $\lVert A \rVert_F$. State whether $A$ is invertible and justify the answer in one sentence.


## Answer policy

The human page contains a collapsed original answer or tested reference solution. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `original-la-foundations`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.